Linkage disequilibrium fine mapping of quantitative trait loci: A simulation study

Recently, the use of linkage disequilibrium (LD) to locate genes which affect quantitative traits (QTL) has received an increasing interest, but the plausibility of fine mapping using linkage disequilibrium techniques for QTL has not been well studied. The main objectives of this work were to (1) measure the extent and pattern of LD between a putative QTL and nearby markers in finite populations and (2) investigate the usefulness of LD in fine mapping QTL in simulated populations using a dense map of multiallelic or biallelic marker loci. The test of association between a marker and QTL and the power of the test were calculated based on single-marker regression analysis. The results show the presence of substantial linkage disequilibrium with closely linked marker loci after 100 to 200 generations of random mating. Although the power to test the association with a frequent QTL of large effect was satisfactory, the power was low for the QTL with a small effect and/or low frequency. More powerful, multi-locus methods may be required to map low frequent QTL with small genetic effects, as well as combining both linkage and linkage disequilibrium information. The results also showed that multiallelic markers are more useful than biallelic markers to detect linkage disequilibrium and association at an equal distance.     

Extent and consistency across generations of linkage disequilibrium in commercial layer chicken breeding populations

Recent studies report a surprisingly high degree of marker-to-marker linkage disequilibrium (LD) in ruminant livestock populations. This has important implications for QTL mapping and marker-assisted selection. This study evaluated LD between microsatellite markers in a number of breeding populations of layer chickens using the standardized chi-square (chi(2')) measure. The results show appreciable LD among markers separated by up to 5 cM, decreasing rapidly with increased separation between markers. The LD within 5 cM was strongly conserved across generations and differed among chromosomal regions. Using marker-to-marker LD as an indication for marker-QTL LD, a genome scan of markers spaced 2 cM apart at moderate power would have good chances of uncovering most QTL segregating in these populations. However, of markers showing significant trait associations, only 57% are expected to be within 5 cM of the responsible QTL, and the remainder will be up to 20 cM away. Thus, high-resolution LD mapping of QTL will require dense marker genotyping across the region of interest to allow for interval mapping of the QTL.     

Linkage disequilibrium in the domesticated pig

This study investigated the extent of linkage disequilibrium (LD) in two genomic regions (on chromosomes 4 and 7) in five populations of domesticated pigs. LD was measured with D' and tested for significance with the Fisher exact test. Effects of genetic (linkage) distance, chromosome, population, and their interactions on D' were tested both through a linear model analysis of covariance and by a theoretical nonlinear model. The overall result was that (1) the distance explained most of the variability of D', (2) the effect of chromosome was significant, and (3) the effect of population was significant. The significance of the chromosome effect may have resulted from selection and the significance of the population effect illustrates the effects of population structures and effective population sizes on LD. These results suggest that mapping methods based on LD may be valuable even with only moderately dense marker spacing in pigs.     

Genome-wide linkage disequilibrium in two Japanese beef cattle breeds

There is little knowledge about the degree of linkage disequilibrium (LD) in beef cattle. This study aims to perform a genome-wide search for LD in Japanese Black and Japanese Brown beef cattle and to compare the level of LD between these two breeds. Parameter D' (the LD coefficient) was used as a measure of LD, and LD was tested for significance of allelic associations between syntenic and between non-syntenic marker pairs. Effects of breed, chromosome, genetic map distance and their interactions with D' were tested based on least squares analyses. Both breeds showed high levels of LD, which ranged over several tens of cM and declined as the marker distance increased for syntenic marker pairs. A rapid decline of the D' value was observed between markers that were spaced 5 and 20 cM apart. LD was significant in most cases for marker pairs <40 cM apart but was not significant between non-syntenic loci. The pattern of LD found in these two breeds was similar to that previously published for dairy cattle. The D' value between breeds was not significantly different (P > 0.05), but the interaction between breed and chromosome was highly significant (P < 0.001). Genetic selection seems to have caused the heterogeneity of the D' values among chromosomes within breed. These results indicate that LD mapping is a useful tool for fine-mapping quantitative trait loci of economically important traits in Japanese beef cattle.     

Levels of linkage disequilibrium in a wild bird population

Population-based mapping approaches are attractive for tracing the genetic background to phenotypic traits in wild species, given that it is often difficult to gather extensive and well-defined pedigrees needed for quantitative trait locus analysis. However, the feasibility of association or hitch-hiking mapping is dependent on the degree of linkage disequilibrium (LD) in the population, on which there is yet limited information for wild species. Here we use single nucleotide polymorphism (SNP) markers from 23 genes in a recently established linkage map of the Z chromosome of the collared flycatcher, to study the extent of LD in a natural bird population. In most but not all cases we find SNPs within the same intron (less than 500 bp) to be in perfect LD. However, LD then decays to background level at a distance 1cM or 400-500 kb. Although LD seems more extensive than in other species, if the observed pattern is representative for other regions of the genome and turns out to be a general feature of natural bird populations, dense marker maps might be needed for genome scans aimed at identifying association between marker and trait loci.     

The extent of linkage disequilibrium in four populations with distinct demographic histories

The design and feasibility of whole-genome-association studies are critically dependent on the extent of linkage disequilibrium (LD) between markers. Although there has been extensive theoretical discussion of this, few empirical data exist. The authors have determined the extent of LD among 38 biallelic markers with minor allele frequencies >.1, since these are most comparable to the common disease-susceptibility polymorphisms that association studies aim to detect. The markers come from three chromosomal regions-1,335 kb on chromosome 13q12-13, 380 kb on chromosome 19q13.2, and 120 kb on chromosome 22q13.3-which have been extensively mapped. These markers were examined in approximately 1,600 individuals from four populations, all of European origin but with different demographic histories; Afrikaners, Ashkenazim, Finns, and East Anglian British. There are few differences, either in allele frequencies or in LD, among the populations studied. A similar inverse relationship was found between LD and distance in each genomic region and in each population. Mean D' is.68 for marker pairs <5 kb apart and is.24 for pairs separated by 10-20 kb, and the level of LD is not different from that seen in unlinked marker pairs separated by >500 kb. However, only 50% of marker pairs at distances <5 kb display sufficient LD (delta>.3) to be useful in association studies. Results of the present study, if representative of the whole genome, suggest that a whole-genome scan searching for common disease-susceptibility alleles would require markers spaced < or = 5 kb apart.     

A comparison of linkage disequilibrium patterns and estimated population recombination rates across multiple populations

Large-scale studies of linkage disequilibrium (LD) have shown considerable variation in the extent and distribution of pairwise LD within and between populations. Taken at face value, these results suggest that genomewide LD maps for one population may not be generalizable to other populations. However, at least part of this diversity is due to some undesirable features of pairwise LD measures, which are well documented for the D' and r2 measures. In this report, we compare patterns of LD derived from pairwise measures with statistical estimates of population recombination rates ( rho ) along a 10-Mb stretch of chromosome 20 in four population samples, comprising East Asians, African Americans, and U.K. and U.S. individuals of western European descent. The results reveal the expected variability of D' within and between populations but show better concordance in estimates of r2 for the same markers across the population samples. Estimates of rho correlate well across populations, but there is still evidence of population-specific spikes and troughs in rho values. We conclude that it is unlikely that a single haplotype map will provide a definitive guide for association studies of many populations; rather, multiple maps will need to be constructed to provide the best-possible guides for gene mapping.     

Linkage disequilibrium in related breeding lines of chickens

High-density genotyping of single-nucleotide polymorphisms (SNPs) enables detection of quantitative trait loci (QTL) by linkage disequilibrium (LD) mapping using LD between markers and QTL and the subsequent use of this information for marker-assisted selection (MAS). The success of LD mapping and MAS depends on the extent of LD in the populations of interest and the use of associations across populations requires LD between loci to be consistent across populations. To assess the extent and consistency of LD in commercial broiler breeding populations, we used genotype data for 959 and 398 SNPs on chromosomes 1 and 4 on 179-244 individuals from each of nine commercial broiler chicken breeding lines. Results show that LD measured by r(2) extends over shorter distances than reported previously in other livestock breeding populations. The LD at short distance (within 1 cM) tended to be consistent across related populations; correlations of LD measured by r for pairs of lines ranged from 0.17 to 0.94 and closely matched the line relationships based on marker allele frequencies. In conclusion, LD-based correlations are good estimates of line relationships and the relationship between a pair of lines a good predictor of LD consistency between the lines.     

The extent of linkage disequilibrium in a large cattle population of western Africa and its consequences for association studies

Several previous studies concluded that linkage disequilibrium (LD) in livestock populations from developed countries originated from the impact of strong selection. Here, we assessed the extent of LD in a cattle population from western Africa that was bred in an extensive farming system. The analyses were performed on 363 individuals in a Bos indicus x Bos taurus population using 42 microsatellite markers on BTA04, BTA07 and BTA13. A high level of expected heterozygosity (0.71), a high mean number of alleles per locus (9.7) and a mild shift in Hardy-Weinberg equilibrium were found. Linkage disequilibrium extended over shorter distances than what has been observed in cattle from developed countries. Effective population size was assessed using two methods; both methods produced large values: 1388 when considering heterozygosity (assuming a mutation rate of 10(-3)) and 2344 when considering LD on whole linkage groups (assuming a constant population size over generations). However, analysing the decay of LD as a function of marker spacing indicated a decreasing trend in effective population size over generations. This decrease could be explained by increasing selective pressure and/or by an admixture process. Finally, LD extended over small distances, which suggested that whole-genome scans will require a large number of markers. However, association studies using such populations will be effective.     

Comparison of Linkage Disequilibrium in Elite European Maize Inbred Lines using AFLP and SSR Markers

Application of association mapping to plant breeding populations has the potential to revolutionize plant genetics. The main objectives of this study were to (i) investigate the extent and genomic distribution of linkage disequilibrium (LD) between pairs of amplified fragment length polymorphism (AFLP) markers, (ii) compare these results with those obtained with simple sequence repeat (SSR) markers, and (iii) compare the usefulness of AFLP and SSR markers for genomewide association mapping in plant breeding populations. We examined LD in a cross-section of 72 European elite inbred lines genotyped with 452 AFLP and 93 SSR markers. LD was significant (p < 0.05) for about 15% of the AFLP marker pairs and for about 49% of the SSR marker pairs in each of the two germplasm groups, flint and dent. In both germplasm groups the ratio of linked to unlinked loci pairs in LD was higher for AFLPs than for SSRs. The observation of LD due to linkage for both marker types suggested that genome-wide association mapping should be possible using either AFLPs or SSRs. The results of our study indicated that SSRs should be favored over AFLPs but the opposite applies to populations with a long history of recombination.     

Characterizing linkage disequilibrium in pig populations

Knowledge of the extent and range of linkage disequilibrium (LD), defined as non-random association of alleles at two or more loci, in animal populations is extremely valuable in localizing genes affecting quantitative traits, identifying chromosomal regions under selection, studying population history, and characterizing/managing genetic resources and diversity. Two commonly used LD measures, r(2) and D', and their permutation based adjustments, were evaluated using genotypes of more than 6,000 pigs from six commercial lines (two terminal sire lines and four maternal lines) at ~4,500 autosomal SNPs (single nucleotide polymorphisms). The results indicated that permutation only partially removed the dependency of D' on allele frequency and that r(2) is a considerably more robust LD measure. The maximum r(2) was derived as a function of allele frequency. Using the same genotype dataset, the extent of LD in these pig populations was estimated for all possible syntenic SNP pairs using r(2) and the ratio of r(2) over its theoretical maximum. As expected, the extent of LD highest for SNP pairs was found in tightest linkage and decreased as their map distance increased. The level of LD found in these pig populations appears to be lower than previously implied in several other studies using microsatellite genotype data. For all pairs of SNPs approximately 3 centiMorgan (cM) apart, the average r(2) was equal to 0.1. Based on the average population-wise LD found in these six commercial pig lines, we recommend a spacing of 0.1 to 1 cM for a whole genome association study in pig populations.     

Evaluation of linkage disequilibrium measures between multi-allelic markers as predictors of linkage disequilibrium between markers and QTL

Effectiveness of marker-assisted selection (MAS) and quantitative trait loci (QTL) mapping using population-wide linkage disequilibrium (LD) between markers and QTL depends on the extent of LD and how it declines with distance in a population. Because marker-QTL LD cannot be observed directly, the objective of this study was to evaluate alternative measures of observable LD between multi-allelic markers as predictors of usable LD of multi-allelic markers with presumed biallelic QTL. Observable LD between marker pairs was evaluated using eight existing measures and one new measure. These consisted of two pooled and standardized measures of LD between pairs of alleles at two markers based on Lewontin's LD measure, two pooled measures of squared correlations between alleles, one standardized measure using Hardy-Weinberg heterozygosities, and four measures based on the chi-square statistic for testing for association between alleles at two loci. In simulated populations with a range of LD generated by drift and a range of marker polymorphism, marker-marker LD measured by a standardized chi-square statistic (denoted chi(2')) was found to be the best predictor of useable marker-QTL LD for a group of multi-allelic markers. Estimates of the level and decline of marker-marker LD with distance obtained from chi(2') were linearly and highly correlated with usable LD of those markers with QTL across population structures and marker polymorphism. Corresponding relationships were poorer for the other marker-marker LD measures. Therefore, when LD is generated by drift, chi(2') is recommended to quantify the amount and extent of usable LD in a population for QTL mapping and MAS based on multi-allelic markers.     

The posterior probability of linkage allowing for linkage disequilibrium and a new estimate of disequilibrium between a trait and a marker

The posterior probability of linkage (PPL) statistic has been developed as a method for the rigorous accumulation of evidence for or against linkage allowing for both intra- and inter-sample heterogeneity. To date, the method has assumed linkage equilibrium between alleles at the trait locus and the marker locus. We now generalize the PPL to allow for linkage disequilibrium (LD), by incorporating variable phase probabilities into the underlying linkage likelihood. This enables us to recover the marginal posterior density of the recombination fraction, integrating out nuisance parameters of the trait model, including the locus heterogeneity (admixture) parameter, as well as a vector of LD parameters. The marginal posterior density can then be updated across data subsets or new data as they become available, while allowing parameters of the trait model to vary between data sets. The method applies immediately to general pedigree structures and to markers with multiple alleles. In the case of SNPs, the likelihood is parameterized in terms of the standard single LD parameter D'; and it therefore affords a mechanism for estimation of D' between the marker and the trait, again, without fixing the parameters of the trait model and allowing for updating across data sets. It is even possible to allow for a different associated allele in different populations, while accumulating information regarding the strength of LD. While a computationally efficient implementation for multi-allelic markers is still in progress, we have implemented a version of this new LD-PPL for SNPs and evaluated its performance in nuclear families. Our simulations show that LD-PPLs tend to be larger than PPLs (stronger evidence in favor of linkage/LD) with increased LD level, under a variety of generating models; while in the absence of linkage and LD, LD-PPLs tend to be smaller than PPLs (stronger evidence against linkage). The estimate of D' also behaves well even in relatively small, heterogeneous samples.     

Estimation of the extent of linkage disequilibrium in seven regions of the porcine genome

Linkage disequilibrium (LD) refers to the correlation among neighboring alleles, reflecting non-random patterns of association between alleles at (nearby) loci. A better understanding of LD in the porcine genome is of direct relevance for identification of genes and mutations with a certain effect on the traits of interest. Here, 215 SNPs in seven genomic regions were genotyped in individuals of three breeds. Pairwise linkage disequilibrium was calculated for all marker pairs. To estimate the extent of LD, all pairwise LD values were plotted against the distance between the markers. Based on SNP markers in four genomic regions analyzed in three panels from populations of Large White, Dutch Landrace, and Meishan origin, useful LD is estimated to extend for approximately 40 to 60 kb in the porcine genome.     

Linkage Disequilibrium Mapping of Morphological, Resistance, and Other Agronomically Relevant Traits in Modern Spring Barley Cultivars

A set of 148 modern spring barley cultivars was explored for the extent of linkage disequilibrium (LD) between genes governing traits and nearby marker alleles. Associations of agronomically relevant traits (days to heading, plant height), resistance traits (leaf rust, barley yellow dwarf virus (BYD)), and morphological traits (rachilla hair length, lodicule size) with AFLP markers and SSR markers were found. Known major genes and QTLs were confirmed, but also new putative QTLs were found. The LD mapping clearly indicated the common occurrence of Rph3, a gene for hypersensitivity resistance against Puccinia hordei, and also confirmed the QTL Rphq2 for prolonging latency period of P. hordei in seedlings. We also found strong indication for a hitherto not reported gene for resistance or tolerance to BYD on chromosome 2, linked to SSR marker HVM054. Our conclusion is that LD mapping is a valuable additional tool in the search for applicable marker associations with major genes and QTLs. Electronic supplementary material Electronic supplementary material is available for this article at and accessible for authorised users.     

Linkage disequilibrium and allele-frequency distributions for 114 single-nucleotide polymorphisms in five populations

Single-nucleotide polymorphisms (SNPs) may be extremely important for deciphering the impact of genetic variation on complex human diseases. The ultimate value of SNPs for linkage and association mapping studies depends in part on the distribution of SNP allele frequencies and intermarker linkage disequilibrium (LD) across populations. Limited information is available about these distributions on a genomewide scale, particularly for LD. Using 114 SNPs from 33 genes, we compared these distributions in five American populations (727 individuals) of African, European, Chinese, Hispanic, and Japanese descent. The allele frequencies were highly correlated across populations but differed by >20% for at least one pair of populations in 35% of SNPs. The correlation in LD was high for some pairs of populations but not for others (e.g., Chinese American or Japanese American vs. any other population). Regardless of population, average minor-allele frequencies were significantly higher for SNPs in noncoding regions (20%-25%) than for SNPs in coding regions (12%-16%). Interestingly, we found that intermarker LD may be strongest with pairs of SNPs in which both markers are nonconservative substitutions, compared to pairs of SNPs where at least one marker is a conservative substitution. These results suggest that population differences and marker location within the gene may be important factors in the selection of SNPs for use in the study of complex disease with linkage or association mapping methods.     

Patterns of linkage disequilibrium and association mapping in diploid alfalfa (M. sativa L.)

Association mapping enables the detection of marker-trait associations in unstructured populations by taking advantage of historical linkage disequilibrium (LD) that exists between a marker and the true causative polymorphism of the trait phenotype. Our first objective was to understand the pattern of LD decay in the diploid alfalfa genome. We used 89 highly polymorphic SSR loci in 374 unimproved diploid alfalfa (Medicago sativa L.) genotypes from 120 accessions to infer chromosome-wide patterns of LD. We also sequenced four lignin biosynthesis candidate genes (caffeoyl-CoA 3-O-methyltransferase (CCoAoMT), ferulate-5-hydroxylase (F5H), caffeic acid-O-methyltransferase (COMT), and phenylalanine amonialyase (PAL 1)) to identify single nucleotide polymorphisms (SNPs) and infer within gene estimates of LD. As the second objective of this study, we conducted association mapping for cell wall components and agronomic traits using the SSR markers and SNPs from the four candidate genes. We found very little LD among SSR markers implying limited value for genomewide association studies. In contrast, within gene LD decayed within 300 bp below an r (2) of 0.2 in three of four candidate genes. We identified one SSR and two highly significant SNPs associated with biomass yield. Based on our results, focusing association mapping on candidate gene sequences will be necessary until a dense set of genome-wide markers is available for alfalfa.     

Analysis of genome-wide linkage disequilibrium in the highly polyploid sugarcane

Linkage disequilibrium (LD) in crops, established by domestication and early breeding, can be a valuable basis for mapping the genome. We undertook an assessment of LD in sugarcane (Saccharum spp), characterized by one of the most complex crop genomes, with its high ploidy level (>or=8) and chromosome number (>100) as well as its interspecific origin. Using AFLP markers, we surveyed 1,537 polymorphisms among 72 modern sugarcane cultivars. We exploited information from available genetic maps to determine a relevant statistical threshold that discriminates marker associations due to linkage from other associations. LD is very common among closely linked markers and steadily decreases within a 0-30 cM window. Many instances of linked markers cannot be recognized due to the confounding effect of polyploidy. However, LD within a sample of cultivars appears as efficient as linkage analysis within a controlled progeny in terms of assigning markers to cosegregation groups. Saturating the genome coverage remains a challenge, but applying LD-based mapping within breeding programs will considerably speed up the localization of genes controlling important traits by making use of phenotypic information produced in the course of selection.     

Linkage disequilibrium inflates type I error rates in multipoint linkage analysis when parental genotypes are missing

OBJECTIVES: Describe the inflation in nonparametric multipoint LOD scores due to inter-marker linkage disequilibrium (LD) across many markers with varied allele frequencies. METHOD: Using simulated two-generation families with and without parents, we conducted nonparametric multipoint linkage analysis with 2 to 10 markers with minor allele frequencies (MAF) of 0.5 and 0.1. RESULTS: Misspecification of population haplotype frequencies by assuming linkage equilibrium caused inflated multipoint LOD scores due to inter-marker LD when parental genotypes were not included. Inflation increased as more markers in LD were included and decreased as markers in equilibrium were added. When marker allele frequencies were unequal, the r2 measure of LD was a better predictor of inflation than D'. CONCLUSION: This observation strongly supports the evaluation of LD in multipoint linkage analyses, and further suggests that unaccounted for LD may be suspected when two-point and multipoint linkage analyses show a marked disparity in regions with elevated r2 measures of LD. Given the increasing popularity of high-density genome-wide SNP screens, inter-marker LD should be a concern in future linkage studies.     

An isochore transition in the NF1 gene region coincides with a switch in the extent of linkage disequilibrium

Whole-genome association studies will be a powerful tool to identify genes responsible for common human diseases. A crucial task for association-mapping studies is the evaluation of the relationship between linkage disequilibrium (LD) and physical distance for the genomic region under study. Since it is known that the extent of LD is nonuniformly distributed throughout the human genome, the required marker density has to be determined specifically for the region under study. These regions may be related to isochores and chromosomal bands, as indicated by earlier cytogenetic findings concerning chiasma distribution in meiosis. Therefore we analyzed the neurofibromatosis type 1 (NF1) gene region on chromosome 17q11.2, which is characterized by a nonuniform LD pattern and an L1-to-H2 isochore transition. Long-range LD within the NF1 gene was found to extend over 200 kb (D' = 0.937) in the L1 isochore, whereas, in the neighboring H2 isochore, no LD is apparent between markers spaced by 26 kb (D' = 0.144). Recombination frequencies derived from the LD are at.00019 (high LD) and.01659 (low LD) per megabase, the latter identical to the average value from segregation analysis. The boundary between these regions coincides precisely with a transition in the GC content of the sequences, with low values (37.2%) in the region with long-range LD and high values (51%) in the other. Our results suggest a correlation between the LD pattern and the isochores, at least in the NF1 region. If this correlation can be generalized, the marker densities required for association studies have to be adjusted to the regional GC content and may be chosen according to the isochores.